In British English, it seems that "because" can always be replaced with "as." Here is an example of "as" meaning "because" in British English:
I popped down to the shops as we were out of loo roll.
In American English, this would translate to:
I went to the store because we were out of toilet paper.
Here is an example of "as" meaning "while" in American English:
I farted loudly as I descended the stairs.
In British English, the preceding sentence would be ambiguous because "as" could mean "while" (the fart coincides with the descent) or "because" (the fart is a result of the descent).
Has this always been true? If "as" has two main meanings ("while" and "because"), which of these was the original? And when was the second meaning added?